Methods and apparatus for signature prediction and feature level fusion

ABSTRACT

A system for signature prediction and feature-level fusion of a target according to various aspects of the present invention includes a first sensing modality for providing a measured data set. The system further includes a processor receiving the measured data set and generating a first k-orthogonal spanning tree constructed from k orthogonal minimal spanning trees having no edge shared between the k minimal spanning trees to define a first data manifold. 
     A method for signature prediction and feature-level fusion of a target according to various aspects of the present invention includes generating a first manifold by developing a connected graph of data from a first sensing modality using a first k-orthogonal spanning tree, generating a second manifold by developing a second connected graph of data from a second sensing modality using a second k-orthogonal spanning tree, and aligning the first manifold and the second manifold to generate a joint-signature manifold in a common embedding space.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 61/054,539, filed May 20, 2008, and incorporates thedisclosure of the application by reference.

BACKGROUND

Generating meaningful joint sensor/signature manifolds includesgenerating a connected graph for subsequent eigenprocessing andembedding. One technique for generating such a graph usesk-nearest-neighbor selection for defining adjacency. However, thistechnique is known to be sensitive to cyclic behavior, and for a smallnumber of neighbors (k) in the graph, portions of the data oftendegenerate into null space. While this technique has been successful inan academic setting, it fails when it is applied in large real-worlddata sets whose individual signatures vary widely.

Nonlinear dimensionality reduction techniques operate under theassumption that Euclidean measures of similarity are meaningful locally,but not globally. Graphs provide a natural mathematical framework fornonlinear dimensionality reduction. Formally, a graph G consists of apair of sets (V, E), where V is a set of vertices and E is a set ofedges. The set of edges denote pairs of elements of V. A path P is anordered sequence of vertices v₁, v₂, . . . , v_(n) with an edgee_(jk)=(v_(j), v_(k)) ⊂ E for all consecutive pairs of vertices in theordered sequence, e_(k)=(v_(k), v_(k+1))⊂ E ∀v_(k), v_(k+1) ⊂ P. A graphG is connected if a path exists between every pair of vertices,3P(v_(k), v_(j)) ∀(v_(k), v_(j))⊂ V. Two vertices are adjacent,v_(n)˜v_(k), if an edge exists between them, e_(jk)=(v_(j), v_(k))⊂ E.

An edge weight function w: V×V→R is a real-valued label associated withthe edge, often representing the edge length or distance between theassociated or adjacent vertices. Two common weight functions used ongraphs are the simple nearest neighbor. Equation (1) and the Gaussian,or heat kernel. Equation (2):

$\begin{matrix}{w_{ij} = \left\{ \begin{matrix}1 & {v_{i} \sim v_{j}} \\0 & {{otherwise};}\end{matrix} \right.} & (1) \\{w_{ij} = \left\{ \begin{matrix}e^{\frac{- {{v_{i} - v_{j}}}^{2}}{a}} & {v_{i} \sim v_{j}} \\0 & {{otherwise}.}\end{matrix} \right.} & (2)\end{matrix}$

When applied to data, both of these functions can generate non-connectedgraphs for small k (where k is the limit on number of nearest neighborsto which these functions are applied; the k neighbors are selected inorder of increasing distance) or small a, where a gives a physical scalefor the heat-kernel approach to defining edge weights (Equation (2)).However, this problem is not detectable until the eigen-decomposition iscomputed, and the existence of a multiplicity of zero-valued eigenvaluesindicates that the graph is not fully connected. The typical solution tothis is to increase either k or a, which often results in suboptimalmanifolds due to loss of local information, which destroys the abilityof the dimensionality-reduction technique to retain the nonlinearcharacteristics of the original data.

The manifold alignment technique published by Ham (J. Ham et al.,“Semisupervised Manifold Alignment,” in R. Cowell and Z. Ghahramani(eds.), Proc. Of the Tenth International Workshop on ArtificialIntelligence and Statistics, pp. 120-127, 2005) depends on the graphbeing completely connected. If the graph components are not connected,the sets of connected subgraphs would be defined in separate eigensystems, and map to each other's null-space by the process. Theresultant embedding is meaningful only for a subset of the data. Toavoid this problem and to ensure that all points are connected, k isincreased to guarantee a connected graph. This leads to problems becausethe goal of the process is to preserve the local neighborhoods, whichcan be destroyed when k is large.

The idea of taking two disparate sensors and projecting them into acommon space has been tried before (D. Marchette et al., “ComparingApples & Oranges: Methods for Comparing the Incomparable,” HawaiiInternational Conference on Statistics and Related Fields (2004)). Thisapproach does not find the underlying manifold of the space first,leading to projections from high dimensions. Another way to executefeature-level fusion is to use joint probabilities and Bayesian networks(S. Ferrari et al., “Demining Sensor Modeling and Feature-Level Fusionby Bayesian Networks”, IEEE Sensors Journal, Vol. 6 (2006)). Thisapproach is problematic in high dimensions because the probabilities arenot known and can only be roughly estimated. Feature fusion can also bedone by combining features from different sensors into a single featurevector (U.S. Pat. No. 6,594,382, entitled “Neural Sensors” and Issued onJul. 15, 2003, to Roger Woodall). But this approach suffers from highdimensionality, as well as from the problem of estimating meaningfulscaling factors between the sensor-specific feature sets.

SUMMARY OF THE EMBODIMENTS

A system for generating a signature manifold of a data set according tovarious aspects of the present invention includes a first sensingmodality for providing a measured data set. The system further includesa processor receiving the measured data set and generating a firstk-orthogonal spanning tree constructed from k minimal spanning treeshaving no edge shared between the A* minimal spanning trees to define afirst data manifold.

A method for signature prediction and feature-level fusion of a targetaccording to various aspects of the present invention includesgenerating a first manifold by developing a connected graph of data froma first sensing modality using a first k-orthogonal spanning tree,generating a second manifold by developing a second connected graph ofdata from a second sensing modality using a second k-orthogonal spanningtree, and aligning the first manifold and the second manifold togenerate a joint-signature manifold in a common embedding space.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

A more complete understanding of the present invention may be derived byreferring to the detailed description and claims when considered inconnection with the following illustrative figures. In the followingfigures, like reference numbers refer to similar elements and stepsthroughout the figures.

FIG. 1 is a missile seeker used in a sensor/target environment;

FIG. 2 is a block diagram of a signature prediction and feature levelfusion system;

FIG. 3 is a flow chart of a method for signature prediction and featurelevel fusion; and

FIG. 4 is an example of a k-orthogonal minimal spanning tree.

Elements and steps in the figures are illustrated for simplicity andclarity and have not necessarily been rendered according to anyparticular sequence. For example, steps that may be performedconcurrently or in different order are illustrated in the figures tohelp to improve understanding of embodiments of the present invention.

DETAILED DESCRIPTIONS OF EMBODIMENTS

Surveillance and missile tracking systems can sense the environmentusing many different sensors, including infrared, video, radar,acoustic, and laser sensors, and are employed in various applicationsfor target detection tracking classification, and in missileapplications, disablement of targets. Identification and verification ofthe target are extremely important. Therefore, several sensors,typically of different modalities, are used in conjunction with eachother. A common coordinate system may be generated to fuse features andpredict signatures for a target using more than one sensing modality.FIG. 1 shows an example of a possible application for methods andapparatus according to various aspects of the present invention,including identifying a target 2 and steering a guided missile 4 to thetarget. The missile 4 may have multiple sensors 12, 18 that communicatewith a steering system 6 to provide control signals that steer themissile 4 to the identified target 2. Data from the sensors 12, 18 areprocessed to aid in the identification and destruction of the target 2by the missile 4. While various aspects of the present invention aredescribed with reference to a particular illustrative embodiment, theinvention is not limited to such embodiments, and additionalmodifications, applications, and embodiments may be implemented withoutdeparting from the present invention.

Various aspects of the present invention relate to characterizing thesubspace spanned by data, and more particularly to a mathematical basisfor feature-level fusion and signature prediction using manifoldalignment applied to data from two or more sensing modalities.Graph-based techniques may be used to characterize the subspace spannedby data By aligning manifolds from different sensing modalities, acommon coordinate system can be generated for feature fusion andcross-modality feature prediction as can be used in reconnaissance andweapon sensors. Sensing modalities may include, but are not limited to,video, infrared and radar.

Referring to FIG. 2, a data fusion system 10 may be configured togenerate a meaningful joint-sensor/signature manifold. A first sensingmodality 12, such as a camera, provides a measured data set 14, such astarget signature data, to a processor 16. The processor 16 generates ak-orthogonal spanning tree for the measured target signature data 14 ofthe first sensing modality 12. At least a second sensing modality 18also provides a second measured data set 20 to the processor 16. Thesecond sensing modality 18 may or may not be the same type as the firstsensing modality 12. For example, the first sensing modality may be acamera providing target signature data relating to images and the secondsensing modality may be a microphone providing target signature datarelating to audio signals. Additional sensing modalities 22 and theirmeasured data sets 24 may also be concurrently used.

The processor 16 processes each measured data set 14, 20 (and possibly24), and generates separate k-orthogonal spanning trees for each of theinput sets of target signature data, defining a first k-orthogonalspanning tree and at least a second k-orthogonal spanning tree. Neitherthe values for k nor the weight function need to be the same across theseparate sensing modality Inputs. The processor 16 determines a graphLaplacian matrix for each of the separate graphs, providing adata-derived estimate of each sensor data's intrinsic manifold. Theindividual graph Laplacian matrices are combined into an overall matrixand the overall matrix is subjected to eigen-decomposition. Alignmentmay comprise deriving a fused low-dimensional joint embedding ofsignatures 26, also called a common coordinate system or a commonembedding space, where certain pre-specified associated points in commonacross the multiple (at least two in this example) measured data setsare constrained to embed to the same coordinate.

Referring to FIG. 3, a method 100 according to various aspects of thepresent invention includes generating a joint-signature manifold forsignature prediction and feature-level fusion for the case of twosensing modalities, measuring a new target signature measured using thefirst sensing modality, and translating the new first sensing modalitytarget signature into the second sensing modality space. While thepresent exemplary embodiment relates to two sensing modalities, anynumber of sensing modalities may be used to build graphs and be embeddedin a common space. A first sensing modality provides measures targetsignatures from a first sensor in a data set 102, and a connected graphmanifold is built in a first sensing modality space using this data setand k-orthogonal spanning trees 106. A second sensing modality providesmeasured target signatures from a second sensor in a data set 104, and aconnected graph manifold is built in a second sensing modality spaceusing this data set and k-orthogonal spanning trees 108. The twoseparate graph manifolds are aligned 110, mapping all the data from thefirst sensing modality data set 102 and ail the data from the secondsensing modality data set 104 to a common joint embedding space 112.

A new (out-of-sample) target signature 114 is measured by the firstsensing modality. Using NyStröm's equation, the new target signature isprojected 116 into the data manifold for the first sensing modality 106,and is assigned coordinates in the common embedding space 112. Since thetwo sensing modalities are co-aligned in the common embedding space, thetarget signatures corresponding to the second sensing modality 120 withsimilar coordinates are found. This information is backprojected intothe original space associated with the second sensing modality 108, ineffect providing a translation 122 of a target signature 114 from thefirst sensing modality space to a set of target signatures in the secondsensing modality space predicting the target data,

Referring to FIG. 4, an exemplary k-orthogonal minimal spanning tree 200comprises k minimal spanning trees, where no vertex is shared betweenthe k graphs. In the present example, k=4. The k-orthogonal spanningtree is constructed through iterative calculation of a minimal spanningtree and removing all edges in the current tree from consideration infuture trees. The result is the construction of a single connectedgraph, even when using small k, with no disjoint subgraphs.

Given edges defined by the k-orthogonal spanning tree computed on thedata, a graph Laplacian matrix L(G) is defined in Equation (3) as:

L(G)=D−W.   (3)

In Equation (3), D consists of a diagonal matrix with elements equal tothe degrees of the vertices of G, i.e., d_(jj)=deg(v_(i)), and W is theweight matrix of G, with elements w_(ij). Specifically, the elementsl_(ij) of L(G) are given by:

$\begin{matrix}{l_{ij} = \left\{ \begin{matrix}{\deg \left( v_{i} \right)} & {{{if}\mspace{14mu} i} = j} \\{- w_{ij}} & {{{if}\mspace{14mu} v_{i}} \sim v_{j}} \\0 & {{otherwise}.}\end{matrix} \right.} & (4)\end{matrix}$

In Equation (4) the degree of a vertex is given by the sum of its edgeweights,

$\begin{matrix}{{\deg \left( v_{i} \right)} = {\sum\limits_{j}\; {w_{ij}.}}} & (5)\end{matrix}$

The graph Laplacian is, by construction, positive semi definite. Ageneral eignvector/eigenvalue problem can be constructed as follows:

Lg=λDg.   (6)

In the solution to Equation (6), the eigenvectors g₁, g₂, . . . , G_(d)corresponding to the smallest d nonzero eigenvalues 0<λ₁≦λ₂≦ . . .≦λ_(d) provide a natural mapping or embedding to a d-dimensionalsubspace. There is always at least one eigenvalue equal to zero, and allzero-valued eigenvalues may be ignored. Mapping may be accomplished byassociating the j-th sample point to the j-th component of theeigenvectors as shown in Equation (7):

f:x _(j)→(g _(j)(j),g ₂(j), . . . ,g _(d)(j)).   (7)

Solving Equation (6) is equivalent to defining a real valued function onthe graph ƒ: V→R such that a cost function, Equation (8), is minimized.The functions {ƒ₁, ƒ₂, . . . , ƒ_(d)} that minimize Equation (8)correspond to the eigenvectors of L as defined in Equation (7).

$\begin{matrix}{{f^{T}{Lf}} = {\frac{1}{2}{\sum\limits_{i,j}\; {\left( {f_{j} - f_{i}} \right)^{2}w_{ij}}}}} & (8)\end{matrix}$

The eigensystem of the graph Laplacian with an appropriate heat kernel,Equation (2), weight function can be analogous to diffusion processes onthe graph and is directly related to a Laplace-Beltrami operator onmanifolds Therefore, the eigensystem of the graph Laplacian provides adata-derived estimate of the data's manifold. Each sensing modality hasa constructed graph that is fully connected and known as a manifold.

Referring again to FIG. 3, the present system may align the data sets110, or manifolds 106, 108, derived for each sensing modality, orsource, 102 and 104. Aligning the manifolds involves deriving a commonembedding space 112 where certain points, called associated pairs(labeled points), are constrained to embed to the same coordinate foraligning the manifolds. This is similar to using control points toperform registration between two images. Though several input sensordata point sets may be used, the present example uses two sensingmodality data point sets, X 102 and Y 104.

The sets of points X and Y are each organized into two disjoint subsets,l and u. The subset l contains labeled points and the subset it containsunlabeled points. Those points belonging to the labeled subset l of theset X have a corresponding point in the labeled subset l of the set Y.L^(X) and L^(Y) are the individual Laplacian matrices of the graphsdefined on the sets X and Y. The graph Laplacian matrix L^(X) can bedecomposed as the following:

$\begin{matrix}{L^{X} = {\begin{bmatrix}L_{ll}^{X} & L_{lu}^{X} \\L_{ul}^{X} & L_{uu}^{X}\end{bmatrix}.}} & (9)\end{matrix}$

In Equation (9), the subscript l denotes point membership in the labeledset and the subscript u denotes point membership in the unlabeled set.There are three distinct combinations: (i) the subscript ll refers toconnections between two labeled points; (ii) the subscript uu refers toconnections between two unlabeled points; and (in) the subscript lnrefers to connections between one labeled point and one unlabeled point.The fourth element, having subscript ul, is simply the transpose of theelement having subscript lu, and thus provides no independentinformation. In analogy with Equation (9) for the graph Laplacian matrixL^(X), the graph Laplacian matrix L^(Y) can be decomposed as:

$\begin{matrix}{L^{Y} = {\begin{bmatrix}L_{ll}^{Y} & L_{lu}^{Y} \\L_{ul}^{Y} & L_{uu}^{Y}\end{bmatrix}.}} & (10)\end{matrix}$

Let ƒ and g denote real-valued functions defined on X and Yrespectively, A

dual-embedding cost function, which is a generalization of Equation (8),is defined to be

$\begin{matrix}{{C\left( {f,g} \right)} = {\frac{{\mu \; {\sum\limits_{i = 1}\; {{f_{i} - g_{i}}}^{2}}} + {f^{T}L^{Z}f} + {g^{T}L^{Z}g}}{{f^{T}f} + {g^{T}g}}.}} & (11)\end{matrix}$

The parameter μ controls the importance of co-locating the pairedpoints, that is, μ→∞ enforces ƒ_(i)=g_(i) for all i⊂l. In this limit,optimizing the C(ƒ, g) given in Equation (11) reduces to minimizing C(h)given by:

$\begin{matrix}{{C(h)} = {\frac{h^{T}L^{Z}h}{h^{T}h}.}} & (12)\end{matrix}$

In Equation (12), h and L^(Z) are defined by:

$\begin{matrix}{{h = \begin{bmatrix}{f_{i} = g_{i}} \\f_{u} \\g_{u}\end{bmatrix}},{L^{Z} = {\begin{bmatrix}{L_{ll}^{X} + L_{ll}^{Y}} & L_{lu}^{X} & L_{lu}^{Y} \\L_{ul}^{X} & L_{uu}^{X} & 0 \\L_{ul}^{Y} & 0 & L_{uu}^{Y}\end{bmatrix}.}}} & (13)\end{matrix}$

The eigenvectors {h₁, h₂, . . . , h_(d)} of L^(Z) in Equation (13)associated with the d smallest positive eigenvalues provide the jointembedding coordinates for the sets X Y. The subspace mapping is definedin Equation (7), but using functions h rather than functions g.

Unlike linear dimensionality reduction techniques, the coordinate systemor embedding defined by a nonlinear dimensionality reduction techniqueis nonparametric in nature. For example, the subspace may becharacterized by the eigenvectors/eigenvalues and the associatedvertices or points which were used to define the eigensystem no modelmay be learned, rather the original points may be retained forsubsequent processing of new data points. The projection of a new datapoint x info a low-dimensional subspace, such as is defined by Equation(7) for the cost functions defined by Equation (8) or Equation (12), isgiven by NyStröm's equation;

ƒ(x)=[ƒ₂(x), . . . , ƒ_(d)(x)]  (14)

and is defined as:

$\begin{matrix}{{f_{i}(x)} = {\frac{1}{\lambda_{i}}{\sum\limits_{j = 1}^{n}\; {h_{ij}{{K\left( {x,x_{j}} \right)}.}}}}} & (15)\end{matrix}$

In Equation (15), K is an appropriate kernel function which defines thesimilarity of the new point x with the n joint-sensor-space samplepoints x_(j), j={1 . . . n}. The Gaussian kernel (similar to Equation(2)) and nearest neighbor kernel (similar to Equation (1)) may be usedas the kernel function K.

Appropriate application of equations (14) and (15) provides an effectiveapproach for mapping new data points into the low-dimensional non-linearsubspace, but care should be taken in use and interpretation ofout-of-sample embedding for off-manifold points. Off-manifold (i.e.distant) points may embed (often to the origin, depending on thekernel), but the embedding is generally not meaningful.

By using k-orthogonal spanning trees as part, of the process forgenerating and then aligning the data manifolds from different, sensingmodalities, the embodiment enables generation of a common coordinatesystem for feature fusion and cross-modality feature prediction. Giventhe joint embedding space and the target signatures embedded therein, itis possible to augment classification algorithms given test signaturesobtained from the multiple sensors. Referring to FIG. 3, it is alsopossible to perform signature prediction, where data 114 (e.g.,target-pose signature) measured in one sensing modality is used topredict the data 122 of the same object in the other sensing modality.

Using a common embedding space, also called a fused object signature

manifold, for signature sets X and F from two heterogeneous co-alignedsensors, the concept of cross-sensor signature prediction reduces to aninference problem in the joint embedding space. The first and seconddata sets X and Y are mapped by way of h (see Equation (13)) into thecommon embedding space. Signature prediction can now comprisequantifying the nature of the other set in the neighborhood of the pointin question.

Given points x ε X, y ε Y, and the k-dimensional joint embeddingfunctions h={h₁, h₂, . . . , h_(d)} (see Equation (13)), define:

D _(h)(x, y)=√{square root over ((h(x)−h(y))^(Y)(h(x)−h(y)).)}{squareroot over ((h(x)−h(y))^(Y)(h(x)−h(y)).)}{square root over((h(x)−h(y))^(Y)(h(x)−h(y)).)}{square root over((h(x)−h(y))^(Y)(h(x)−h(y)).)}  (16)

This is the Euclidean distance in the common embedding space, whichshould be meaningful in some neighborhood about a point on the manifold.Within the context of meaningful mappings (as discussed above withrespect to off-manifold points), the mapping of object signaturesbetween sensors is as simple as selecting the nearest neighbors in theother set.

Feature-level signature prediction can be accomplished by taking a setof signatures from a target object not represented in the training setor common embedding space, computing the embedding of the set usingEquation (15), and in the subspace finding neighboring points belongingto the other sensor modalities. Then, for those neighboring points, goback to the original sensor data corresponding to those subspace points.These sensor data points give the neighborhood of signature translationspredicted by the manifold-alignment technique.

The joint signature manifold alignment also enables feature-level fusionfor

classification. In a target classification system that, for illustrativeexample, uses concurrently operating video and radar sensing modalities,current methods Involve decision-level fusion. This method combines theresults of two independent classifiers, one for video and one for radar.It is possible for the two classifiers to report different targets, forexample a ‘dog’ from a classifier operating on the data from one sensorand a ‘rock’ from a classifier operating on data from another sensor,and the fusion algorithm would have no way to fuse these twoclassifications. According to the joint-signature manifold alignment ofthe embodiment, features from the video and radar sensors are combinedbefore a classification is made. In the current example, the manifoldalignment would be applied to both the video and the radar data,co-registering the data in the combined embedding space. Therefore, thefeatures are the embedding space coordinates. A classifier is thenapplied in the embedding space and a single decision is made, forexample either ‘dog’ or ‘rock’. Only a single classification output isproduced from the data from the two sensors. An advantage to thefeature-level fusion of the embodiment is that deficiencies in onesensing modality can be compensated in the other sensing modality,leading to more robust results.

Systems and methods according to various aspects of the presentinvention may be adapted for signature prediction and feature-levelfusion that allows a measured data set, target signatures measured byone sensing modality, to predict what a target will look like to anothersensing modality, where the second sensing modality is not necessarilymeasuring the same physical properties as the first sensing modality,and to map features from heterogeneous sensing modalities into a commonembedding space. The measured data set of target signatures, associatedwith a sensing modality, define a manifold, which is described using agraph generated by orthogonal spanning trees. The separatesensor-signature manifolds are then co-aligned and nonlineardimensionality reduction is performed to derive a common embedding spacewhere certain data from the different sensing modalities are constrainedto embed to the same coordinate.

Orthogonal spanning trees are used to generate a connected graph that isused to align the manifolds from different sensing modalities. A minimalspanning tree is a connected graph with an associated minimal pathlength as defined by a weight function. A k-orthogonal spanning treeconsists of k minimal spanning trees, where no edge is shared betweenthe k graphs. The k-orthogonal spanning tree is constructed by iterativecalculation of the minimal spanning tree and removing all edges in thecurrent tree from consideration for future trees. In this way, connectedgraphs can be constructed using small k while still preserving nonlinearstructural information.

By aligning the data manifolds from different sensing modalities, thepresent exemplary systems and methods generate a common coordinatesystem for feature fusion and cross-modality feature prediction. Thepresent exemplary systems and methods may provide a robust approach forsignature prediction and feature-level fusion that provides thegeneration of a connected graph to prevent degenerate mappings, even forsmall k or small a. The present systems and methods may also preservenonlinear structural information that can be lost due to degeneratemappings. Additionally, target signatures that are not represented inthe training set can be embedded into the common embedding space, andcorresponding signatures from other sensing modalities can be estimated.Because the embodiments are able to preserve any nonlinear structuralinformation as represented by the signature data, the relationshipbetween novel signatures and the nonlinear embedding is retained,enhancing the meaningfulness of the resultant predicted signatures ofother sensor modalities as defined by the common embedding space

In the foregoing specification, the invention has been described withreference to specific exemplary embodiments. Various modifications andchanges may be made, however, without departing from the scope of thepresent invention as set forth in the claims. The specification andfigures are illustrative, rather than restrictive, and modifications areintended to be included within the scope of the present invention.Accordingly, the scope of the invention should be determined by theclaims and their legal equivalents rather than by merely the examplesdescribed.

For example, the steps recited in any method or process claims may beexecuted in any order and are not limited to the specific orderpresented in the claims. Additionally, the components and/or elementsrecited in any apparatus claims may be assembled or otherwiseoperationally configured in a variety of permutations and areaccordingly not limited to the specific configuration recited in theclaims.

Benefits, other advantages and solutions to problems have been describedabove with regard to particular embodiments; however, any benefit,advantage, solution to problem or any element that may cause anyparticular benefit, advantage or solution to occur or to become morepronounced are not to be construed as critical, required or essentialfeatures or components of any or all the claims.

The terms “comprise”, “comprises”, “comprising”, “having”, “including”,“includes” or any variation thereof, are intended to reference anon-exclusive inclusion, such that a process, method, article,composition or apparatus that comprises a list of elements does notinclude only those elements recited, but may also include other elementsnot expressly listed or inherent to such process, method, article,composition or apparatus. Other combinations and/or modifications of theabove-described structures, arrangements, applications, proportions,elements, materials or components used in the practice of the presentinvention, in addition to those not specifically recited, may be variedor otherwise particularly adapted to specific environments,manufacturing specifications, design parameters or other operatingrequirements without departing from the general principles of the same.

1. A system for generating a signature manifold of a data set,comprising; a first sensing modality for providing a first measured dataset; a processor responsive to the first sensing modality and adaptedto: receive the first measured data set of the first sensing modality;and generate a first k-orthogonal spanning tree constructed from kminimal spanning trees having no edge shared between the k minimalspanning trees to define a first data manifold.
 2. The system as claimedin claim 1, further comprising: a second sensing modality for providinga second measured data set; and wherein the processor is responsive tothe second sensing modality and is adapted to receive the secondmeasured data set of the second sensing modality and generate a secondk-orthogonal spanning tree constructed from k minimal spanning treeshaving no edge shared between the k minimal spanning trees to define atleast a second data manifold, where k used for the second data manifolddoes not have to equal k used for the first data manifold.
 3. The systemas claimed in claim 2, wherein the processor is adapted to create acommon embedding space aligning the first and second data manifolds. 4.The system as claimed in claim 3, wherein the low-dimensional embeddingis used by the processor to predict a data measurement in the secondsensing modality from a data measurement from the first sensingmodality,
 5. A system for predicting target signatures in a secondsensing modality using target signatures measured from a first sensingmodality, comprising: a first sensing modality providing measured targetsignatures; a second sensing modality providing measured targetsignatures; and a processor responsive to the first and second sensingmodalities, wherein the processor is adapted to generate: a firstmanifold generated by embedding the measured target signatures from thefirst sensing modality; a second manifold generated by embedding themeasured target signatures from the second sensing modality; a commonembedding space generated by aligning the first and second manifolds inthe processor; and a set of predictions of the target signature from thesecond sensing modality generated by the measured target signatures ofthe first sensing modality.
 6. The system as claimed in claim 5, whereinthe processor is further adapted to generate an out-of-sample data pointmeasured in the first sensing modality and projected in the firstmanifold defining a new target signature, wherein the new targetsignature is embedded in the common embedding space and used to find anew target signature in the second manifold.
 7. A method for signatureprediction and feature-level fusion of a target, comprising: generatinga first manifold by developing a connected graph of data from a firstsensing modality using a first k-orthogonal spanning tree; generating atleast a second manifold by developing a connected graph of data from atleast a second sensing modality using a second k-orthogonal spanningtree in which the k-value does not have to equal any of the values usedfor generating other manifolds; and aligning the first manifold and theat least a second manifold to generate a joint-signature manifold in acommon embedding space.
 8. The method as claimed in claim 7, whereingenerating the first and second manifolds by developing a connectedgraph of data comprises: calculating k orthogonal minimal spanning treesby removing all edges in a current minimal spanning tree fromconsideration in subsequent minimal spanning trees to ensure no vertexis shared between the k minimal spanning trees.
 9. The method as claimedin claim 8, wherein aligning the first manifold and the at least asecond manifold further comprises deriving a common coordinate spacewith associated pairs of data in each of the first and second manifoldsconstrained to embed to the same coordinate.
 10. The method as claimedin claim 9, further comprising augmenting a classification algorithmgiven test signatures in the joint-signature manifold.
 11. The method asclaimed in claim 9, further comprising predicting a signature of thetarget in the at least a second sensing modality using thejoint-signature manifold and the first manifold.
 12. The method asclaimed in claim 11, further comprising comparing a set of signaturesnot represented in the joint-signature manifold to the joint-signaturemanifold to predict target signatures across the first and the at leasta second sensing modalities.
 13. The method as claimed in claim 12,further comprising: mapping the first manifold into a common embeddingspace; mapping the at least a second manifold into the common embeddingspace; and mapping the target between the first and at least secondmanifolds.
 14. A method for feature-level fusion of at least two sensingmodalities, comprising: developing a connected graph of feature datafrom a first sensing modality using a first k-orthogonal spanning treeto define a first manifold; developing a connected graph of feature datafrom at least a second sensing modality using a second k-orthogonalspanning tree, k-value not necessarily equal to any of the k-values usedfor generating other manifolds, to define at least a second manifold;aligning the first and at least a second manifold to define a commonembedding space; embedding an out-of-sample first sensing modalityfeature vector in the first manifold and the common embedding space;embedding an out-of-sample second sensing modality feature vector in atleast a second manifold and the common embedding space; determiningembedding space coordinates for the embedded out-of-sample featurevectors in the common embedding space; applying a classifier to theembedded out-of-sample feature vectors from the embedding spacecoordinates.
 15. The method as claimed in claim 13, further comprising:projecting an out-of-sample first sensing modality feature vector in thefirst signature manifold; finding a set of neighboring points for theout-of-sample feature vector in the common embedding space for the atleast a second sensing modality; and backprojecting the set ofneighboring points into at least a second signature manifold; whereinthe backprojected set of neighboring feature vectors providesfeature-level signature prediction for the at least a second sensingmodality in the common embedding space
 16. A system for communication oftarget signature information between sensor platforms, comprising: twoor more sensor platforms each consisting of one or more sensors and oneor more processors; a first sensor providing measured target data toprocessor 1; projecting an out-of-sample first sensing modality featurevector in the first signature manifold; finding a set of neighboringpoints for the out-of-sample feature vector in the common embeddingspace for the at least a second sensing modality; and backprojecting theset of neighboring points into at least a second signature manifold;processor 1 communicating at least the second signature manifold resultsto the at least processor 2 on other platforms for processing.
 17. Thesystem as claimed in claim 16, further comprising a predicted datameasurement in the at least a second data manifold using the fusedobject signature manifold from target data measured in the first sensor.18. The system as claimed in claim 16, further comprising a classifierdetermined from a target feature embedded in the first data manifold andthe fused object signature manifold; the target feature embedded in theat least a second data manifold and the fused object signature manifold;and embedded space coordinates for the embedded target feature in thefused object signature manifold are determined from a comparison of theembedded target feature in the first, at least a second and the fusedobject signature manifolds; wherein the classifier is applied to thetarget signatures derived from the embedded space coordinates.